Various numerical full-wave electromagnetic analysis techniques have been used to characterize electromagnetic scattering by passive arbitrary three-dimensional structures. The analysis is generally based on solving Maxwell's electromagnetic (EM) equations for the surface under analysis. Because of the need to capture the signature response from complex structures, such as aircraft, the analysis has been approximated and automated using the method of moments (MoM) and are well suited to the problem only after characterizing the non-planar surface as consisting of a first mesh of finite planar surfaces or cells on the structure. For example is U.S. Pat. No. 6,353,801 granted to Sercu, et al. on Mar. 5, 2002, or R. Harrington, Origin and Development of the Method of Moments for Field Computation, IEEE Antennas and Propagation Magazine, June 1990, which references are incorporated herein by this reference.
The basic physics of electromagnetic fields is governed by Maxwell's equations. With computational methods derived from integral equations, a three-dimensional boundary-value problem reduces to a two-dimensional problem over the boundary of the domain of interest, i.e. MoM. However, even with a significant reduction in the number of unknowns, the computational cost of generating the full system matrix and the difficulties in solving the linear equations often makes this approach costly and slow. It is also difficult to formulate the appropriate IE for geometrically complex inhomogeneous structures, possibly requiring a nontrivial derivation of a geometry-dependent Green's function.
A basic understanding of the underlying principles and technologies of finite element simulators is important for generating successful interconnect designs using such simulators. A designer using the finite element tool typically has some understanding of the underlying MoM technology. The designer may select initial mesh parameters (number of cells/wavelength, number of cells/transmission line width, edge meshing on/off, etc.) that will characterize the structure to within an acceptable accuracy. Setting these parameters is always a trade off between simulation accuracy and simulation speed. The larger the number of cells, the more accurate the solution, but slower and more expensive, in terms of computer resources, the solution becomes. For instance, using a PC running at approximately 1 GHz a 50-wavelength linear scatterer using 10 computational cells per wavelength would require days of CPU time. Thus, there is an unmet need in the art for a method and computer program for predicting electromagnetic scattering more efficiently.